1.3soln - Solutions to problems from section 1.3 4. Let u =...

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Unformatted text preview: Solutions to problems from section 1.3 4. Let u = bracketleftbigg 3 2 bracketrightbigg and v = bracketleftbigg 2- 1 bracketrightbigg . Display the following vectors using arrows on an xy-graph: u , v ,- v ,- 2v , u + v , u- v , and u- 2v . Solution: 6. Write a linear system which is equivalent to x 1 bracketleftbigg- 2 3 bracketrightbigg + x 2 bracketleftbigg 8 5 bracketrightbigg + x 3 bracketleftbigg 1- 6 bracketrightbigg = bracketleftbigg bracketrightbigg Solution:- 2 x 1 + 8 x 2 + x 3 = 0 , 3 x 1 + 5 x 2- 6 x 3 = 0 . 10. Write a vector equation that is equivalent to the following linear sys- tem: 4 x 1 + x 2 + 3 x 3 = 9 , x 1- 7 x 2- 2 x 3 = 2 , 8 x 1 + 6 x 2- 5 x 3 = 15 . Solution: x 1 4 1 8 + x 2 1- 7 6 + x 3 3- 2- 5 = 9 2 15 12. Is b a linear combination of a 1 , a 2 , and a 3 where a 1 = 1- 2 2 , a 2 = 5 5 , a 3 = 2 8 , b = - 5 11- 7 ? Solution: Answering this question is the same as answering whether or not the linear system with augmented matrix 1 0 2- 5- 2 5 0 11 2 5 8- 7 is consistent. Lets row reduce....
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This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.

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1.3soln - Solutions to problems from section 1.3 4. Let u =...

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